The vertical vibration of thin circular or sectorial plate under small flexivity theory is further investigated, and the natural boundary condition problem at the center of circle is discussed. The mistakes in several relative literature are analyzed and corrected. In the process of using variable-separated method to seek the solution of vibration on sectorial plate, the results are unrelative to the order of solving the angular and radical direction function, the classical views on boundary condition agree with the outcomes of variational method. It is concluded that the traditional theories of thin plate on solving the vertical small vibration problems are all proper up to present.